Casimir interaction between inclined metallic cylinders

TL;DR

This paper investigates how the Casimir force between inclined metallic cylinders varies with orientation and separation, revealing unique decay behaviors and providing both numerical and analytical insights for different boundary conditions.

Contribution

It provides a comprehensive analysis of the orientation dependence of Casimir interactions between inclined cylinders across various boundary conditions and separation regimes.

Findings

At large distances, the interaction decays slowly, similar to parallel cylinders.

At small distances, the interaction scales as that of two spheres.

Numerical results agree with analytical predictions at intermediate distances.

Abstract

The Casimir interaction between one-dimensional metallic objects (cylinders, wires) displays unconventional features. Here we study the orientation dependence of this interaction by computing the Casimir energy between two inclined cylinders over a wide range of separations. We consider Dirichlet, Neumann and perfect metal boundary conditions, both at zero temperature and in the classical high temperature limit. For all types of boundary conditions, we find that at large distances the interaction decays slowly with distance, similarly to the case of parallel cylinders, and at small distances scales as the interaction of two spheres (but with different numerical coefficients). Our numerical results at intermediate distances agree with our analytic predictions at small and large separations. Experimental implications are discussed.